The analysis methods described herein and in the above related patents and applications use a pulsed burst or pulse of energy that is designed to excite the nuclei of a particular nuclear species of a sample being measured (the protons, or the like, of such sample having first been precessed in an essentially static magnetic field); in other words the precession is modified by the pulse. After the application of the pulse there occurs a free induction decay (FID) of the magnetization associated with the excited nuclei. That is, the transverse magnetization associated with the excited nuclei relaxes back to its equilibrium value of zero. This relaxation produces a changing magnetic field which is measured in adjacent pickup coils. A representation of this relaxation is the FID curve.
The analysis methods described herein and in the above related patents and applications are to decompose the FID waveform into a sum of separate time function equations. The coefficients of these equations are derived from the FID by use of a Marquardt-Levenberg (M-L) iterative approximation that minimizes the Chi-Squared function--a technique well known in the art. Some of the time function equations found useful are: Gaussians; exponentials; Abragams, defined herein by (Gaussian)*(sin(t))*(1/t); modified Gaussian, defined herein by ((Gaussian)*(cos(sqrt(t)))), and trigonometric. From these time functions a set of parameters is calculated. Some of these parameters are ratios of the y-axis intercepts, decay times (or time constants of decay) for each of the time curves, and the cross products and reciprocals thereof. Statistical modeling techniques are used to select a subset of these terms to form a regression model, and regression coefficients are computed for this subset.
But, relating these previously mentioned parameters, quantitatively and qualitatively, back to the species of target nuclei is required. In the above referenced patent applications, the system is calibrated with known samples, and a regression equation is generated which relates the parameters to the types, properties and quantities of the target nuclei. An unknown sample is introduced, the time functions are derived via the M-L iteration, and the parameters are calculated. The parameters are "regressed" via the regression equation to yield the types, properties and quantities of target nuclei in the unknown sample. That is, the measured parameters from the unknown FID are used with the regression equation, and the types, properties and quantities in the unknown sample are determined. It is to be understood that the multidimensional regression equation may not be graphically represented, and that the regression equation may be non-linear. As a simple regression technique example, consider that the grade point average of each of the students at a college were related to that student's SAT score and high school standing (forming a three dimensional space). The line formed is a "regression line" (which may be graphed). A new student's grade point average may be predicted by placing the student's SAT and high school standing on the "regression line" and "reading" the grade point average.
The sample temperature may form the basis for another regression parameter. It is therefore necessary to carry out nmr measurements with the sample at a certain pre-fixed temperature. This is handled by controlling the temperature of the sample. A limitation exists since any temperature difference between the sample and the sample chamber and the local environment will cause the sample temperature to change during the measurement. This changing temperature creates errors in the nmr results which may become significant--particularly in industrial, essentially on-line usage (e.g., manufacturing or transport processes or the like with repetitive sampling and feedback or feed forward process control). Such errors have been observed, for example, when measuring and then predicting the solids content in processed cheese, and, similarly, various melt flow rate measurements in polyolefins, such as melt index (MI), flow rate ratio (FRR) and melt flow (MF).
It is well established that the T2 relaxation rate in solutions or melts is directly dependent on the viscosity of the solution or melt. Polymer viscosity measurements, in either solution or melts, can therefore be performed by nmr measurements and since viscosity is related to the average molecular weight of polymers, a correlation between T2 and molecular weight can be established.
In the solid phase, however, the restricted molecular motion shortens the T2 value dramatically, and in the extreme of crystalline or near rigid amorphous polymers the T2 values are very short and show no indication of yielding molecular weight information.
Care must be taken when measuring and controlling sample temperature. Probes, infrared devices and other known temperature measuring devices for on-line temperature measurements need to be designed and constructed to not materially interfere with setting and maintaining a given sample temperature. Accordingly, it is an object of this invention to provide a thermal environment where a sample under test is maintained at a controlled settable temperature.
It is an object of this invention to effect a sample measurement of polymer materials at a mobility enhancing temperature that enhances precision and reliability for viscosity, molecular weight, melt index and melt flow. Herein, molecular weight, melt index and melt flow, are closely related. It is another object of this invention to measure the temperature change of the sample and adjust heater means such that there is essentially no sample temperature change during the nmr measurement time period. Another object of this invention is to gain the benefit of the higher mobilities of polymers and the enhanced nmr response which is found when polymer material is melted but without actually melting the material. It is another object of this invention to maintain the sample chamber temperature about equal to the mobility enhancing temperature of the successive samples such that the successive samples will maintain about the same temperature during the nmr measurement time period. It is to be understood that the process temperature may change slowly with time as a function of ambient temperatures or process conditions.
Another object is to correlate known viscosities and/or melt index or melt flow (which are related to average molecular weights) with the measured nmr parameters at or around the mobility enhancing temperature for amorphous polymers, crystalline polymers and semi-crystalline polymers (see below). Such correlations are used to determine the calibration coefficients for predicting unknown viscosity and/or melt index or melt flow for an unknown sample.